Solve for $x$ and $y$ using elimination. ${x-6y = -29}$ ${-4x-5y = -58}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${4x-24y = -116}$ $-4x-5y = -58$ Add the top and bottom equations together. $-29y = -174$ $\dfrac{-29y}{{-29}} = \dfrac{-174}{{-29}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-6y = -29}\thinspace$ to find $x$ ${x - 6}{(6)}{= -29}$ $x-36 = -29$ $x-36{+36} = -29{+36}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {-4x-5y = -58}\thinspace$ and get the same answer for $x$ : ${-4x - 5}{(6)}{= -58}$ ${x = 7}$